Central banks around the world are going to new lengths to boost their economies, underscoring both the importance and limits of monetary policy in a global economy plagued by paltry growth and unsettled markets.

The Bank of Japan on Friday joined a host of European peers in setting its key short-term interest rate below zero. The move, long denied as a possible course by the bank’s governor, came a week after the European Central Bank president indicated he was ready to launch additional monetary stimulus in March—and...